Characterization of sequential warped product gradient Ricci-Bourguignon solitons

Abstract

In this paper, we study the characterization of sequential warped product gradient Ricci-Bourguignon solitons. First, we derive applications of some vector fields like torse-forming vector field, torqued vector field and conformal vector field on Ricci-Bourguignon solitons. Next, we show that a RicciBourguignon soliton becomes an almost quasi-Einstein manifold for a torse-forming vector field. Later, we obtain the inheritance properties of the Einstein-like sequential warped product gradient Ricci-Bourguignon almost soliton of class type P,A,B. Further, we establish that when the manifold is complete, the potential function depends only on M1 and M3 must be an Einstein manifold. We also show that the warping functions for a gradient Ricci-Bourguignon soliton sequential warped product are constants under some certain conditions.